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To many people, the choice has become as polarizing as Democrat or Republican, Giants or Patriots, Federer or Nadal. These days, you either own an Apple iPhone or you're a holdout, in which case you most likely make calls and send texts with a Galaxy S-III phone made by Samsung Electronics.

While there are hundreds of models to choose from, the smartphone war increasingly is a two-horse race between
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(ticker: AAPL) and Samsung Electronics (005930.Korea). Together, these two companies will sell 49% of the planet's smartphones this year, but account for nearly all the profits, and the Web overflows with noisy opinions about whose is superior. Investors face a more intriguing choice: Which will be the better stock to own over the next year?

Both are winners in their own right. Each stock has more than tripled since 2009, but still is staggeringly cheap: Apple sits on $29 billion of cash, pays a 2% dividend yield, but fetches just 10.5 times projected 2013 profits -- well below its median of 28 times over the past decade. Samsung's Seoul-listed shares trade at just 6.7 times projected profits. Both are roundly revered: 56 of the 64 analysts who cover Apple urge you to buy its shares, while 47 of 48 who follow Samsung suggest you do the same for that stock. Apple has the planet's biggest stock-market value, while Samsung is the reigning world champion in terms of technology revenue. It holds other titles as well, such as world's largest TV maker, biggest LCD-panel manufacturer, and No. 2 chip maker, behind
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(INTC).

So who'll come out on top? The contrarian in me wants desperately to make a case for Samsung, which leapt 12 places in BrandZ's 2012 ranking of top 100 global brands and still ended up at just No. 55 -- it has so much room to improve! In contrast, rooting for Apple seems about as original and odious as cheering for the New York Yankees.

But while Samsung may be the underdog, Apple is the more underappreciated stock. That gives Apple the edge in a bout between these two heavyweights -- a winner not by knockout, but by decision. Yes, Earth's No. 1 brand just may be its most misunderstood company. Officials at both concerns declined interview requests, but since Apple peaked at a record above $702 mid-September, its stock has corrected 25%, to about $526. Concerns were already rife that the Cupertino, Calif., tech giant had lost its creative dazzle after the 2011 death of its chief executive genius, Steve Jobs, and recent missteps have only exacerbated those fears. A petty decision to drop
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s (GOOG) maps from its new iPhone made Apple seem unusually fearful of its competition. Well-publicized labor abuses at Apple's Asian suppliers gave the impression that it was losing control of its supply chain, and things got worse when Apple couldn't make enough new iPhones to meet the clamorous demand. Smelling blood and eager to depose the king, the mainstream media rushed to trumpet Apple's decline.

Things got uglier after Apple reported fiscal fourth-quarter results in late October. While revenue grew 27% and profit expanded 24%, Apple beat analysts' targets by the slimmest margin in years. Management told investors to expect per-share earnings of just $11.75 this quarter, well below $13.87 a year ago. It also cut projected gross margins from 40% to 36%, which money managers took as a sign that Apple is losing its competitive edge. The word on Wall Street was that Apple had slipped from hypergrowth to merely healthy growth, and that it was time to bolt.

That strategy shifted when Apple began selling tablets in 2010. Here was a new market that Apple helped create and which had no entrenched competitor. This time, Apple's priority was to grab as much market share as it could, and make it tougher for new entrants to join the fray. So it priced tablets more aggressively, at least by Apple's standards; iPads' 32% margins are well below its corporate average. As a result, two years after the iPad was born, Apple still sells two out of every three tablets worldwide.

Apple's ultimate goal, of course, is to build a large, recurring base of devotees. We think of Apple as a tech and consumer stock, but the way it keeps users hooked and coming back for more, it might as well be a drug maker -- albeit one with 43% return on equity. Studies show that people who buy, say, an iPhone are likely to buy an iPad or MacBook or music and movies from the iTunes store -- fully inhabiting the cozy universe Apple creates. "The lifetime value of that is huge," Ursillo says, "which is why Apple is willing to take a little margin erosion up front to build that installed customer base."

CRITICS FRET ABOUT Apple's front-loaded business model: It makes money selling gadgets and not from post-sale services. That creates pressure to keep selling more units, quarter after quarter. "But what's underappreciated is the annuity-like nature of its business," says Josh Spencer, who manages the T. Rowe Price Global Technology Fund. "Apple's built-in replacement cycle is such that customers locked into its ecosystem reliably upgrade and buy new devices every few years." Case in point: iPhones' purchase prices are heavily subsidized by phone carriers, and customers begin lusting after the latest models even before their phone contracts expire every two years.

The cult of Apple can only grow. Apple has about 255 phone-carrier partners in 114 countries -- less than, say, Research In Motion's 580 carriers in 165 countries. Deutsche Bank analyst Chris Whitmore reckons it can reach 1.8 billion subscribers worldwide. Judging by the number of phones and tablets sold over the past two years, he estimates that Apple has penetrated just 10% of its addressable market. "Apple has plenty of room to run, in terms of greater market penetration, as well as incremental carrier additions," Whitmore argues, starting with the launch of the iPhone 5 in 100 countries by December. His price target for the stock: $800.

Having nudged down investors' expectations, Apple has quietly refreshed all its major products, introducing a new iPhone 5, a fourth-generation iPad, the iPad Mini, and an upgraded MacBook Pro. This new lineup, robust demand, and low expectations should produce a very merry Christmas.

ACROSS THE PACIFIC, Samsung Electronics is no slouch. The flagship unit of the Samsung Group once was known as a staid maker of chips, display panels, and household appliances. That changed in 2010, when it unveiled the Galaxy line of smartphones in Asia. Within 45 days of the phones' U.S. launch, more than a million had been sold. Today, Samsung ships more units than anyone else -- its market share jumped to 31% this year from 3.4% in 2009, largely at the expense of has-beens like Nokia and Research In Motion.

Samsung, too, has many fans. Walter Price, who co-manages the Allianz RCM Technology Fund, thinks the smartphone trend is maturing in the developed world, and that higher growth will come next from developing countries. "That should benefit Samsung more than Apple over the next year, since the lower price points of Samsung phones will help it grab share in emerging markets," says Price. He also owns Apple stock, but has been buying Samsung's Korean shares for qualified investors, along with its London-listed depositary shares (SMSN.U.K.).

Among manufacturers, Samsung is Apple's worthiest foe. Smartphones drive two-thirds of its profits, but it also makes its own chips and display panels, which gives it tremendous control over its product.

Samsung also has a formidable silent partner. It is the world's biggest maker of smartphones that run on Android software, which Google created and gave away free to drum up a market for its mobile ads. Today, Android owns 66% of the market for smartphone operating systems, dwarfing the 19% for Apple's iOS software. And because Samsung doesn't pay for its operating software, it can afford to make cheaper devices that help it dominate the mid- to low-end smartphone market.

In contrast, Apple controls both its hardware and software, and can give its customers a more cohesive experience. Apple's fate also isn't hitched to another ambitious competitor the way Samsung's is. For now, Google's search business is so lucrative that it isn't rushing into manufacturing, but its recent purchase of Motorola's handset unit has to worry Samsung.

"There are a lot of Android makers out there, even if Samsung is the biggest right now. So what Samsung offers is less unique to Google than Google to Samsung," says T. Rowe Price's Spencer. "People are saying about Samsung what they once said about Nokia at its peak -- it has scale, great manufacturing, unit volume, better costs, and it dominates the mid- to lower end of the market. But look at Nokia now." Once the global leader in wireless phones, the Finnish company dropped to No. 7 in smartphones in the third quarter, according to research firm Gartner.

If anything, the recent push by Google and Microsoft to make their own devices validates Apple's vertically integrated model. Apple's control of its ecosystem and user experience lets it charge premium prices, says Canaccord Genuity analyst T. Michael Walkley. That's why Apple accounts for just 19% of smartphone units shipped worldwide but rakes in 68% of the operating income.

THE APPLE VERSUS SAMSUNG DRAMA also is playing out in courtrooms across the globe. A San Jose jury this year ordered Samsung to pay Apple $1 billion for infringing certain design patents, but Apple has lost ground in other courts from the U.K. to Korea. Apple investors should be relieved it has recently settled with rivals from Nokia to
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(2498.Taiwan), essentially extracting royalties and licensing pacts in return for dropping litigation.

"From a business standpoint, it makes sense to settle with smaller rivals," says Manotti Jenkins, an intellectual-property litigator at Valorem Law Group. "You avoid paying expensive litigation fees, and generate royalties and revenue that can go toward the fight against Samsung."

If more makers of Android phones start paying royalties to Apple, Android won't seem so free after all. Still, both sides could lose in a long legal brawl. Apple, which buys chips and display panels from Samsung, has been looking to other suppliers, while Samsung is pushing back against the below-market pricing and fat margins Apple demands.

"Apple requires more capacity for its custom processors that are exclusively made by Samsung. However, since it has no long-term commitment beyond the end of 2013, Samsung is refusing to spend literally billions of dollars" to add capacity, notes Bernstein analyst Mark Newman. "The risk for Samsung is idle capacity; the risk for Apple is not enough processors for iPhones and iPads in the second half of 2013."

Escalating its fight, Samsung is running attack ads spoofing the cult of Apple. Samsung knows what it's like to have an image problem. It's still perceived as a maker of commoditized chips, says James Thom, a Singapore-based portfolio manager of Aberdeen Asset Management, even if chips drive just 16% of operating profits.

Samsung also owns controlling stakes in various affiliates with a combined book value of several billion dollars. The founding family holds a 15% stake.

Seoul-based Macquarie analyst Daniel Kim expects Samsung's second-generation Galaxy Note II, a smartphone-tablet hybrid, to sell twice as well over its life cycle as the first-generation device, which chalked up 13 million sales. But the S-III's major design edge -- a large 4.8-inch screen -- is being blunted by ever-larger screens on rival phones, plus the trend to make tablets smaller and easier to tote around.

Samsung also benefited from being the only big manufacturer with new phones on sale last quarter, which helped profit jump 91%, year over year. Its smartphone unit's 19% operating margin last quarter was the highest in two years. Can the Korean titan keep that up in the face of new competition?

While Apple's rabid growth will slow, that isn't necessarily a disaster; IBM shares went on a tear after that company became a mature tech giant. Apple's per-share profit is still expected to rise by double-digit percentages, and it has quietly started to pay a dividend and buy back stock. With 6% of its vast market value in cash, and only 20% of its earnings slotted to pay dividends -- well below Microsoft's 32% -- Apple has many options for rewarding its shareholders.

Nonetheless, Apple still trades at a 20% discount to the overall market. "Ultimately, this game is moving forward, based on research and development and design -- rather than manufacturing efficiency," says Ursillo. In other words, while Samsung makes phones we use, Apple makes what we didn't know we wanted.